Problem: Rewrite as a simplified fraction. ${3.8\overline{91} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3891.9191...\\ 10x &= 38.9191...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3853}$ ${x = \dfrac{3853}{990}} \text{or} {3 \dfrac{883}{990}}$